in 1975, szemeredi proved that any set of integers of positive density must contain arbitrarily long arithmetic progressions. this result solved a 40 year old conjecture of erdos and turan. furthermore, it was one of the main ingredients used by green and tao in their proof that the primes contain arbitrarily long arithmetic progressions. in this talk we will discuss the easiest case of szemeredi's theorem: arithmetic progressions of length 3.